On a conjecture of M. R. Murty and V. K. Murty

被引：0
|
作者：
Ding, Yuchen [1 ]
机构：
[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2023年 / 66卷 / 02期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Primes; Bombieri-Vinogradov theorem; Dichotomy;
D O I：
10.4153/S0008439522000650
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let omega(*)(n) be the number of primes p such that p - 1 divides n. Recently, M. R. Murty and V. K. Murty proved that x(log log x)(3 <<) Sigma(n <= x) omega(*) (n)(2 <<) x log x. They further conjectured that there is some positive constant C such that Sigma (n <= x) omega(*) (n)(2) similar to C x log x, as x -> infinity . In this short note, we give the correct order of the sum by showing that Sigma (n <= x) omega(*) (n)(2) asymptotic to x log x,
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页码：679 / 681
页数：3
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